Year: 2012
Communications in Mathematical Research , Vol. 28 (2012), Iss. 2 : pp. 121–126
Abstract
It is well known that the problem on the stability of the solutions for Fredholm integral equation of the first kind is an ill-posed problem in $C[a, b]$ or $L^2 [a, b]$. In this paper, the representation of the solution for Fredholm integral equation of the first kind is given if it has a unique solution. The stability of the solution is proved in the reproducing kernel space, namely, the measurement errors of the experimental data cannot result in unbounded errors of the true solution. The computation of approximate solution is also stable with respect to $‖·‖_C$ or $‖· ‖_{L^2}$. A numerical experiment shows that the method given in this paper is stable in the reproducing kernel space.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2012-CMR-19051
Communications in Mathematical Research , Vol. 28 (2012), Iss. 2 : pp. 121–126
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 6
Keywords: Freholm integral equation ill-posed problem reproducing kernel space.